Q147 / 180 · JIPMER 2017 · Physics

You are given resistance wire of length 50 cm and a battery of negligible resistance. In which of the following cases is largest amount of heat generated?

  • A
    When the wire is connected to the battery directly
  • B
    When the wire is divided into two parts and both the parts are connected to the battery in parallel.
  • Correct answer
    C
    When the wire is divided into four parts and all the four parts are connected to the battery in parallel.
  • D
    When only half of the wire is connected to the battery.

Solution

Let $R$ be the resistance of the wire (a) $H_1=\frac{V^2 t}{R}$ (b) Resistance of each part will be $R$ / 2. When they are connected in parallel, the resistance will be $R / 4$. Hence, $H_2=\frac{4 v^2 t}{R}$ (c) In case of four wires connected in parallel, the resistance will be $R$ / 8 $\therefore H_3=\frac{8 V^2 t}{R}$ (d) $H_4=\frac{V^2 t}{[R / 2]}=\frac{2 V^2 \cdot t}{R}$ Hence, largest amount of heat will be generated in case of four parts connected in parallel.

Hence, the correct answer is option: 'C'.

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